Question

The density of diamond is 3.52 g/ml and that of graphite is 2.25 g/ml. The formation free energy (ag) of diamond is 2.90 kj/mol and that of graphite is zero at 298.15 k. Find the pressure at which diamond and graphite coexist in equilibrium at 298.15 k.

Answer 1

Explanation:

each phase (graphite or diamond) you can write

μ=μ∘+∫PP∘VmdP

at constant T.

We are asked to find the pressure P=Peq at which carbon coexists in the two phases (the Gibbs free energy is equal in both) so that

μ(diamond)=μ(graphite)

This leads to

Δμ∘=−∫PeqP∘ΔVmdP

and, since Δμ∘=ΔfG∘m, ultimately to the expression you provided:

ΔfG∘m=−∫PeqP∘ΔVmdP

The approximation you are allowed to make at this point is that the solids are incompressible, such that their Vm are constant with change of pressure. It follows that

ΔfG∘m=−ΔVm∫PeqP∘dP=−ΔVm(Peq−P∘)

which can be solved for Peq:

Peq=−ΔfG∘mΔVm+P∘